Kim, Sitae (2016-12). Nonlinear Response and Bifurcations Analysis of Rotor-Fluid Film Bearing Systems. Doctoral Dissertation. Thesis uri icon

abstract

  • Nonlinear response, bifurcations and stability of rotor-fluid film bearing systems are studied using various numerical investigation schemes such as autonomous/non-autonomous shooting, arc-length continuation, direct numerical integrations, Poincar? sections, Lyapunov exponents, etc. Two types of hydrodynamic bearings, a floating ring bearing (FRB) and a tilting pad journal bearing (TPJB), are employed in this study. The nonlinear characteristic of each bearing is analyzed as supports of a rigid rotor system as well as a flexible rotor system. Depending on the existence of the unbalance force on the rotor/disks, autonomous (free vibration) and non-autonomous responses (mass unbalanced excitation) are both identified, and the nonlinear reaction force produced on the lubricant layer is obtained using the finite element method. In addition to isoviscosity lubricants, thermo-hydrodynamic lubricant model is developed to investigate thermal effects on rotordynamic bifurcations; in the procedure, a variable viscosity Reynolds equation and the energy equation are solved simultaneously. For computation efficiency in the analytical bifurcation study, an advanced shooting algorithm, which is combined with the deflation theory and the parallel computing strategy, is proposed for both the autonomous and the non-autonomous cases. In the study with flexible rotors, the finite element based beam models are employed and the model reduction technique such as Component Mode Synthesis is utilized to condense the system degree of freedom. This dissertation consists of four main discussions regarding: 1) nonlinear response and bifurcations of a rigid rotor supported by FRBs; 2) effects of a thermo-hydrodynamic (THD) FRB model on rotordynamic bifurcations; 3) nonlinear response and bifurcations of a rigid rotor supported by TPJBs; 4) extension of study to general, complex, multi-mass rotor beam models. In case 1), multiple coexistent solutions and bifurcation scenarios are identified, and those are depended on the ratio of floating ring length to diameter (L/D). Numerical illustrations regarding jumps between two stable limit cycles and quenching large vibrations are demonstrated, and chaos is investigated with the aid of Lyanpunov exponent. In case 2), the Hopf bifurcation onset is strongly dependent on thermal conditions, and the saddle node bifurcation points are significantly shifted compared to the isothermal model. In addition, the unbalanced responses stability and bifurcation onsets are highly reliant on the lubricant supply temperature. In case 3), loci of bifurcations are identified, and heavily loaded bearings and/or high unbalance force may induce consecutive transference of response in forms of synchronous to sub-synchronous, quasi-periodic responses and chaotic motions. The periodic doubling bifurcations, saddle node bifurcations and corresponding local stability are reliably determined by selections of pad preload, pivot offset, and lubricant viscosity sets. In case 4), two industrial applications such as a turbocharger supported by FRBs and an eight-stage centrifugal compressor supported by TPJBs are numerically analyzed. The turbocharger shows that torus appears with Neimark-Sacker bifurcation events and the motions are dominant in the high speed ranges (>60,000rpm). In the compressor, sub-/super-synchronous motions are identified other than the x1 synchronous response, and the appearance of each harmonic is highly depended on the selection of pad preload and pivot offset.
  • Nonlinear response, bifurcations and stability of rotor-fluid film bearing systems are studied using various numerical investigation schemes such as autonomous/non-autonomous shooting, arc-length continuation, direct numerical integrations, Poincar? sections, Lyapunov exponents, etc. Two types of hydrodynamic bearings, a floating ring bearing (FRB) and a tilting pad journal bearing (TPJB), are employed in this study. The nonlinear characteristic of each bearing is analyzed as supports of a rigid rotor system as well as a flexible rotor system. Depending on the existence of the unbalance force on the rotor/disks, autonomous (free vibration) and non-autonomous responses (mass unbalanced excitation) are both identified, and the nonlinear reaction force produced on the lubricant layer is obtained using the finite element method. In addition to isoviscosity lubricants, thermo-hydrodynamic lubricant model is developed to investigate thermal effects on rotordynamic bifurcations; in the procedure, a variable viscosity Reynolds equation and the energy equation are solved simultaneously. For computation efficiency in the analytical bifurcation study, an advanced shooting algorithm, which is combined with the deflation theory and the parallel computing strategy, is proposed for both the autonomous and the non-autonomous cases. In the study with flexible rotors, the finite element based beam models are employed and the model reduction technique such as Component Mode Synthesis is utilized to condense the system degree of freedom.
    This dissertation consists of four main discussions regarding: 1) nonlinear response and bifurcations of a rigid rotor supported by FRBs; 2) effects of a thermo-hydrodynamic (THD) FRB model on rotordynamic bifurcations; 3) nonlinear response and bifurcations of a rigid rotor supported by TPJBs; 4) extension of study to general, complex, multi-mass rotor beam models. In case 1), multiple coexistent solutions and bifurcation scenarios are identified, and those are depended on the ratio of floating ring length to diameter (L/D). Numerical illustrations regarding jumps between two stable limit cycles and quenching large vibrations are demonstrated, and chaos is investigated with the aid of Lyanpunov exponent. In case 2), the Hopf bifurcation onset is strongly dependent on thermal conditions, and the saddle node bifurcation points are significantly shifted compared to the isothermal model. In addition, the unbalanced responses stability and bifurcation onsets are highly reliant on the lubricant supply temperature. In case 3), loci of bifurcations are identified, and heavily loaded bearings and/or high unbalance force may induce consecutive transference of response in forms of synchronous to sub-synchronous, quasi-periodic responses and chaotic motions. The periodic doubling bifurcations, saddle node bifurcations and corresponding local stability are reliably determined by selections of pad preload, pivot offset, and lubricant viscosity sets. In case 4), two industrial applications such as a turbocharger supported by FRBs and an eight-stage centrifugal compressor supported by TPJBs are numerically analyzed. The turbocharger shows that torus appears with Neimark-Sacker bifurcation events and the motions are dominant in the high speed ranges (>60,000rpm). In the compressor, sub-/super-synchronous motions are identified other than the x1 synchronous response, and the appearance of each harmonic is highly depended on the selection of pad preload and pivot offset.

publication date

  • December 2016